What is the maximum number of electrons allowed in the n=4 principal energy level?

The maximum number of electrons that can occupy a principal energy level is determined by the formula (2n^2), where (n) is the principal quantum number. For the fourth principal energy level (n=4), you simply substitute 4 into the formula:

[

2(4^2) = 2(16) = 32

]

This calculation indicates that the fourth energy level can hold a maximum of 32 electrons. Each principal energy level is capable of holding a greater number of electrons as you move to higher levels, primarily because higher levels have more subshells and orbitals available.

In this case, the correct answer reflects the fundamental principles of quantum mechanics regarding electron configurations and the distribution of electrons within an atom. The other choices offer numbers that do not align with the calculation based on the principal energy level, which is vital for understanding how electrons are organized in an atom. Understanding this can aid in grasping concepts such as chemical bonding and the periodic trends that arise from electron configurations.